具有跟踪鲁棒性能的H∞最优预见控制

摘要

A robust H∞ preview control problem is proposed for a class of uncertain discrete-time systems. A new method is de-rived to construct an augmented error system, avoiding applying the difference operator to the time-varying matrix, and simplify the augmented error system. Then for the augmented error system of the uncertain system, the problem of guaranteed cost robust H∞ con-trol is considered via a state feedback with integral and preview actions. The sufficient condition for the existence of the robust H∞ con-troller and H∞ state feedback controller design methods are presented. The condition can be realized by solving a linear matrix inequal-ity optimization problem. By putting the controller obtained into the original system, we can get the preview controller. Moreover,intro-ducing an integrator makes the closed-loop system robustly track the reference signal without steady-state error. The effectiveness of the proposed method is shown by numerical simulation.%研究了一类不确定离散时间系统的鲁棒H∞预见控制问题。其中采用一种新的方法构造扩大误差系统，避免对时变的系数矩阵取差分，从而成功构造简化的扩大误差系统。然后针对所求得的不确定系统的扩大误差系统，通过引入带有预见作用的状态反馈，研究鲁棒H∞保成本控制问题，得到确保鲁棒H∞控制器存在的充分条件及H∞状态反馈控制器的设计方法。该条件可以通过求解一个线性矩阵不等式优化问题而实现。所得控制器回到原系统就得到带有预见作用的最优预见控制器。而且，通过引入积分器，实现闭环系统对目标值信号的鲁棒无静差跟踪。最后的数值算例说明了本文理论的有效性。